Good morning again Nate, as I posted below BEFORE you can size the wire you FIRST have to decide how many Amps of current you will supply to the outbuilding ??
NEXT you have to decide if you want to direct bury multiconductor cable such as UF or USE etc. etc. ORRRRRRRRRRR to use buried conduit with individual conductors such as copper wire type THWN??
NEXT use Aluminum or Copper conductors ??
NEXT compute Line Voltage Drop and if excessive upsize cables
FINALLY consult ampacity charts for the conductors you have chosen TO GET YOUR ANSWER OF WHAT SIZE CABLE IS REQUIRED
NOTE As different types of cable,,,,,, different methods such as direct bury or enclosed in conduit,,,,,,,,different distances,,,,,,,,copper or aluminum conductors,,,,,,,all make a difference, the size you need may or may NOT be the same as someone else used. Of course what someone here used if given the same service requirements ???? might be the same as what you need !!!!!! Your choice take your pick
If you google wire ampacity charts you will get hundreds of hits and below is ONLY ONE SEARCH START so just be aware to consider all the above so you use the correct chart.. I would err on using too large cable versus too small cable myself to allow for upgrades PLUS reduce line voltage drop and while a 60 Amp service may well get you by, Id consider running a 100 Amp service to allow for upgrades.
Compute current requirements, decide on service size, compute distance, compute line voltage drop, decide what type of cable, direct burial or conduit, CONSULT AMPACITY CHARTS that match your chosen cable and method, install a SUB PANEL with separate insulated and isolated Neutral and Ground Buss, provide proper Grounding at sub
Sorry I cant spoon feed you any easy answer not knowing current, distance, type of cable and method selected and wire etc. etc. etc. Where fire and life safety are concerned (do NOT take my word for it) you might want to at least consider consulting the NEC, professional electricians or engineers, or any applicable local authority in addition to the advice offered here (me included)
John T Best wishes be safe
Cable Ampacity Charts